#!/usr/bin/python
# -*- coding: utf-8 -*-

"""Project Euler Solution 069

Copyright (c) 2011 by Robert Vella - robert.r.h.vella@gmail.com

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and / or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
"""

import cProfile
from euler.numbers.advanced_math import totients
from euler.list_functions import max_by, index


def get_answer():
    """Question:
    
    Euler's Totient function, φ(n) [sometimes called the phi function], is used
    to determine the number of numbers less than n which are relatively prime 
    to n. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and 
    relatively prime to nine, φ(9)=6.
    
    It can be seen that n=6 produces a maximum n/φ(n) for n ≤ 10.
    
    Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum.
    """
    
    #Return the result.
    return max_by(
                 lambda index_value : (index_value.index + 1.0) 
                                        / index_value.value,
                 index(totients(1000000))
                ).index + 1
        
        
if __name__ == "__main__":
    cProfile.run("print(get_answer())")
